While walking and driving in heavy traffic in daily life requires paying attention to other surrounding moving objects, how simultaneously performing an attention demanding task affects the visual control of goal-directed steering remains unknown. Here we examined how different attentional loads affected people's steering toward a goal at both low and high travel speeds. The display (113°H×88°V) simulated a participant traveling at a walking speed of 2 m/s or a driving speed of 15 m/s over a texture ground for 10 s. Participants used a joystick to control the curvature of their traveling path to steer toward a red post target. Concurrently, participants visually tracked one dot (low attentional load) or three dots (high attentional load) among eight dots that randomly moved inside a red circle (radius 3.5°) on top of the target post. Participants' virtual heading had a constant 10° offset from their straight ahead such that steering to center the target at straight ahead would result in a constant 10° heading error. Across nine participants, while the tracking accuracy of low attentional load was not affected by travel speed, the tracking accuracy of high attentional load decreased from 84%±2% (mean±SE) to 74%±1% as travel speed increased from 2 m/s to 15 m/s. For the steering performance in the trials with accurate tracking response, peak path curvature decreased and mean heading error averaged across the first 4-s steering increased with attentional load at both travel speeds. However, after 4-s steering, heading error converged to participants' optimal performance at each travel speed and was not affected by the attentional load. We conclude that participants have more difficulty in dealing with high attention demanding task at high than low travel speed. Attentional load affects the early stage of steering control but does not affect the final heading error.